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Chapter 9: Problem 60

An object falls at a rate of \(100 \mathrm{ft} / \mathrm{s}\) immediately prior to the time that the parachute attached to it opens. The final descent rate with the chute open is \(10 \mathrm{ft}\) ts. Calculate and plot the speed of falling as a function of time from when the chute opens. Assume that the chute opens instantly, that the drag coefficient and air density remain constant, and that the flow is quasisteady.

Short Answer

Expert verified
The plot of the falling speed as a function of time would show a sudden drop from 100 ft/s to 10 ft/s at the moment the parachute opens (\( t = 0 \)). It can be modeled as a piecewise function.

Step by step solution

01

Determine Initial Conditions

The object is falling at a rate of 100 ft/s just before the parachute opens. After the chute opens, it reduces its speed to 10 ft/s instantly.
02

Formulate Speed Function

Since the speed changes instantly from 100 ft/s to 10 ft/s as soon as the parachute opens, we can represent this as a piecewise function:\[v(t)=\begin{{cases}} 100, & \text{{if }} t < 0 \\ 10, & \text{{if }} t \geq 0 \end{{cases}}\] where \( t = 0 \) is the moment the parachute opens.
03

Plot the Speed as a Function of Time

Create a time vector that represents the time before and after the parachute opens. You need two separate intervals, one for \( t < 0 \) and one for \( t \geq 0 \). Plot the function \( v(t) \) using these values. It will result in a step function with a sudden drop from 100 ft/s to 10 ft/s at \( t = 0 \) which indicates the instant the parachute opens.

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